Yes but they are still just four year terms. Appointments were made in 2006, 2010, and now 2014 (Bernanke, Bernanke, and now Yellen).
If we are talking about Presidential power over the economy, you cannot simply say a President's impact is restricted to investor's reactions to his political policies.
In fact the Republican and Democratic similarity in monetary policy is one of the exact reasons why the Parties are in essence very similar to each other at the end of the day. That stems from the President's appointments of chairmen who continue the same monetary policies.
If you elected a man like Rand Paul president, tell me he wouldn't appoint someone radically different as the chairperson of the Fed.... then tell me the President has no impact on the economy. No, things would start changing rapidly around here.